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Later, William will make a Skype web call to two homeless people from Scotland who are working in Holland.

The royal couple will also travel to Dumfries House in Ayrshire.

The 18th century mansion was bought,
along with its contents and adjoining land, by a consortium led by the
Prince of Wales in June 2007.

Charles, known as the Duke of
Rothesay in Scotland, will join his son and daughter-in-law as the
Manoukian Foundation, a new outdoor centre for uniformed youth services
and schools, is opened in the grounds.

The visit will be marked by a
fly-past of three Typhoons from 6 Squadron, RAF Leuchars - a base close
to St Andrews University in Scotland where William and Kate first met as
students.

The couple will then travel to
Barrow-in-Furness, Cumbria, to learn about the new Astute Class of
nuclear powered submarines being built for the Royal Navy by BAE
Systems.

At the Emirates Arena, William and Kate met Games organisers and budding athletes, before unveiling a commemorative plaque to mark their visit.

The couple delighted onlookers by stopping to chat, and William accepted a little girl's request for a kiss from a prince.

Four-year-old Shona Ritchie was dressed in her favourite green and gold princess outfit complete with a gold crown as she stood outside the arena with her family.

Her mother, Karen Ritchie, 34, from Croftfoot, Glasgow, said Shona had waited all morning to ask William for a kiss but, as he leaned over, she became shy.

'She's been dressed up like that since 6am today and we've been here waiting since nine,' Mrs Ritchie said.

'But when she finally plucked up the courage to ask him, she got really shy and pulled away. As he leaned in to kiss her on the forehead she pulled away and got really shy.

Wills takes to the hockey pitch during his visit - mirroring his wife's expertise on the hockey field during a pre-Olympics visit to a school last year

Though she didn't play today, Kate is a keen hockey player and hit the field on a pre-Games visit to the Olympic park in March last year, left, and also during a visit to her former school, St Andrews, right

'This is the quietest she's been all day.'

Kate also stopped to talk to Shona, who gave the Duchess a red flower she had picked out of her mother's vase at home.

Seven-year-old Audrey Grevemberg, the daughter of Glasgow 2014 chief executive David Grevemberg, gave the couple a big silver gift bag with Commonwealth Games jumpers inside.

William accepted the gift and knelt down to speak to the girl while Kate smiled.

When asked if she enjoyed meeting the royal couple, Audrey said she did.

Kate also chatted to teenagers who started learning to pole vault three days ago as part of an Easter holiday course.

Iona Menzies, 14, from Glasgow, said: 'It was such an honour to meet her. She's so pretty in real life.

'It was quite nerve-wracking but she was really encouraging and said we should keep working at it.

'She said she had never seen the pole vault before so it was nice to be able to show her it up close.'Rachel Campbell, also 14, from Erskine, Renfrewshire, said: 'She was really friendly and just asking us how difficult it is.

Kate chats to a little girl who presents the duchess with a rose outside the Donald Dewar Leisure Centre where she is set to launch a new project for their charity. The Royal Foundation of The Duke and Duchess of Cambridge and Prince Harry is partnering with Glasgow Sport and the Hunter Foundation on a new pilot as part of its national Coach Core initiative

Supporters bestow Kate with cuddly toys and flowers on the visit, which saw Kate greet hundreds of well-wishers on the streets of the Scottish city

The duchess accessorised her coat with her trusty suede boots. Under her tartan coat the hemline of a black skirt or dress was just visible

'I was nervous but my heartbeat is calming down now.'

The Duchess gave Scott Connal, 13, from Lenzie, Glasgow, a round of applause as he completed his vault.

'I do lots of athletics so I'm used to people clapping at big competitions but never from royalty, it was really inspiring,' he said.

Mrs Ritchie said: 'She said Shona
looked very pretty and asked her if she had picked the flower from her
garden, but Shona told her she got it from my vase in the house and she
thought that was very funny.'

Kate is given a flower by a local girl named Shona - who had earlier allowed the
Prince to look at her flower but would not give it to him, saying she was saving it for Kate

...and the little girl proved not to be such a fan of William, recoiling as the prince goes in for a kiss

The Duke and Duchess also watched pole vaulters, badminton players and a netball match.

They were treated to a performance from the Glasgow 2014 mascot, Clyde, and Clyde's dance crew.

Kate
later met Clyde and his designer, 12-year-old Beth Gilmour, from
Cumbernauld. It emerged that the cheeky thistle mascot had earlier asked
if he could pat Kate's bump.

Glasgow
2014 marketing manager Samantha Jones said: 'Clyde doesn't speak but he
was gesturing to Kate about her baby as if to congratulate her.

'Before the visit he was asking if he could pat the bump, but we told him no.

'When he was signalling to her about the baby, she just laughed and said "Oh yes, the baby. Thank you very much."

Blooming: The Duchess of Cambridge was glowing as she arrived at the Emirates Arena in Glasgow today

The Duchess of Cambridge pays a visit to the Emirates Arena Leisure Centre in Glasgow this morning

William and Kate, known in Scotland as the Earl and Countess of Strathearn, arrive in Glasgow this morning

Beth, who won a school competition to become the official mascot designer, gave Kate a book named Captain Bristle's Thistle, which tells the story of Clyde.

'I never thought I would win the competition in the first place so meeting royalty was really unexpected, but an honour,' she said.

William later donned headphones to play DJ at a homeless centre for young people.The crowd who gathered to meet the Duke were delighted when he agreed to a crash course in mixing on the decks.

He tried his hand at 'scratching' but claimed it was harder than his day job flying a helicopter.

'I think I should come better prepared next time,' he said after his attempt at mixing Run DMC's It's Like That with another record, a collection of beats and samples.

The Duchess meanwhile turned producer as she called 'cut' during a filming session, one of several workshops available for youngsters at the Quarrier's Stopover Project on Glasgow's southside.

Kate reassured the camera-shy 'actors' and applauded when they finished their pieces.

Later she admitted that knitting was so far not one of her strong points when a resident presented her with a woollen hat for her child along with a teddy bear and babygro.

She said: 'I've been trying to knit and I'm really bad. I should be asking for tips.'

She told 17-year-old Caitlin Coffield: 'It's very sweet of you, I'll keep it safe for the big day.'

The Stopover Project provides short-term accommodation and support to 16 to 25-year-olds.The centre has beds for 14 needy young people who as well as being homeless often have alcohol or drug addiction problems or mental health issues.

The centre works with other agencies to help them tackle their issues and find a permanent home.

Sometimes they stay for weeks, while others take refuge at the centre for up to a year.

The Duke is patron of Centrepoint, another charity that has been providing support for rough sleepers for decades.

Kate's Scottish look was courtesy of the British family-run design company moloh.

The firm has a boutique in Tetbury, close to Charles's Gloucestershire home, and another in Pimlico in central London.

The Duchess's £425 pure wool blue and grey plaid coat, called a Worker's Coat, was created by Caroline Smiley, designer and founder of moloh,
which is celebrating its 10th anniversary this year.

A spokeswoman for the company said Kate has worn a belt from the firm in the past.

She said: 'She's worn the brand before a few years ago but it's great to see she's a loyal fan.

'This coat is from our collection released this year. Only 20 have been made, so once they've gone, they've gone.'

English Women's Clothing: The Gloucestershire and Pimlico-based shop where Kate bought her £425 tartan coat

It is not the first time Kate had shopped at moloh - she has previously worn a belt from the brand. A moloh spokesman said: 'She's worn the brand before a few years ago but it's great to see she's a loyal fan'

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Kate Middleton: Duchess of Cambridge wears very short tartan coat as she joins William in Scotland